Short Answer 
The problem involves breaking down a force of 15 N at an angle into its horizontal (F cos θ) and vertical (F sin θ) components. Given that the horizontal component is 4.5 N, the angle θ is calculated using cos θ = 0.3, resulting in θ = 72.5° above the horizontal.
Step 1: Understand the Force Components
In physics, when a force is applied at an angle, it can be broken down into two components: the horizontal component and the vertical component. For a force of magnitude F = 15 N at angle θ from the horizontal, these components are defined as follows:
- Horizontal component: F cos θ
- Vertical component: F sin θ
Step 2: Set Up the Equation for the Horizontal Component
Given that the horizontal component of the force is 4.5 N, we can create an equation to find the angle θ. This leads us to the equality where we substitute the known values:
- Equation: F cos θ = 4.5 N
- Substituting values: 15 N cos θ = 4.5 N
This simplifies to cos θ = 0.3.
Step 3: Calculate the Angle θ
To find the angle θ, we apply the inverse cosine function to the determined value:
- Calculation: θ = cos⁻¹(0.3)
- Result: This leads us to the final angle of θ = 72.5° above the horizontal.